[Physics] Expectation value vs most probable value of radius in ground state of hydrogen

probabilityquantum mechanicsquantum-measurements

What is the difference when we calculating expectation value for example in hydrogen atom in the ground state? The expectation value is 1.5*Bohr radius while the probability density has a max at Bohr radius. Does expectation value takes into account many measurements?

Best Answer

Suppose you measure something with outcome “1” four times, outcome “2” once, and outcome “3” once. The most probable outcome is “1” but the average is 9/6=1.16. The most probable outcome need not be the average, and indeed the average may not even be a possible outcome.